High thermoelectric efficiency realized in SnSe crystals via structural modulation

Crystalline thermoelectrics have been developed to be potential candidates for power generation and electronic cooling, among which SnSe crystals are becoming the most representative. Herein, we realize high-performance SnSe crystals with promising efficiency through a structural modulation strategy. By alloying strontium at Sn sites, we modify the crystal structure and facilitate the multiband synglisis in p-type SnSe, favoring the optimization of interactive parameters μ and m*. Resultantly, we obtain a significantly enhanced PF ~85 μW cm−1 K−2, with an ultrahigh ZT ~1.4 at 300 K and ZTave ~2.0 among 300–673 K. Moreover, the excellent properties lead to single-leg device efficiency of ~8.9% under a temperature difference ΔT ~300 K, showing superiority among the current low- to mid-temperature thermoelectrics, with an enhanced cooling ΔTmax of ~50.4 K in the 7-pair thermoelectric device. Our study further advances p-type SnSe crystals for practical waste heat recovery and electronic cooling.

the experimental structures at elevated temperatures (from 300 K to 873 K) deriving from the refined SR-XRD data.

Cmcm phases and multiband simulations.
Due to the non-parabolic feature of valence band, we adopted the Kane band model to evaluate the transport properties, including Seebeck coefficient and carrier mobility.
The relaxation time (op) of polar optical phonon-electron scattering can be expressed as 3 : where s and  are static and high frequency dielectric constant and set to 170 and 720, respectively, and 0 is the vacuum dielectric constant.  is a function of reduced energy (), and it is defined as 3 : f (, )the Fermi-Dirac distribution function: Based on above discussions, the total relaxation can be obtained. The carrier concentration, carrier mobility, Seebeck coefficient and Lorenz number of single Kane band model can be calculated 3 : where mb * is the single valley effective mass (mb * = (mx * my * mz * ) 1/3 , md * is density of states (DOS) effective mass (md * = Nv 3/2 mb * ), Nv is degeneracy of valence band (Nv = 2 S4 for each band valley), and mI * is conductance effective mass (mI * = 3/(1/mx * +1/my * +1/mz * )).
For multiple valleys participated in transport, total carrier concentration (ntot), the total carrier mobility (tot), total Seebeck coefficient (Stot), and total Lorenz number (Ltot) can be expressed as: were calculated, and we finally obtained the simulated 3D curves shown in Fig. 1.

Calculation for the heat capacity (Cp) based on Debye model.
Based on the Debye model, we considered the individual contributions of phonons and the effects of thermal expansion, to the total heat capacity of SnSe system 5, 6 . The total heat capacity, Cp,tot, as a function of temperature, can be written as: where Cp,ph and Cp,D represent the phonon heat capacity capacity and the effects of lattice dilation on the heat capacity capacity, respectively.
Here, due to the Debye assumption and elastic wave approximation, the phonon heat capacity capacity Cp,ph can be obtained as: (S18) where B is the isothermal bulk modulus, α is the linear coefficient of thermal expansion, and ρ is the sample density (all dependent on temperature) (67). Based on the above discussion, we obtained total heat capacity for all samples from Debye model. It should be noted that the electrons also contribute to the heat capacity, as Cp,ele. However, since the effect of dilation is mostly phononic in origin, as Cp,ph is much larger than Cp,ele, therefore, the contribution from electrons was not taken into account.

Calculations of average ZT (ZTave).
Among a given temperature range (300 -773 K), the average ZT value (ZTave) is given by: where Th and Tc represent the hot and cold side temperature, respectively. In this work, the Tc is 300K, and Th is 773K.
directions and atomic positions of Sn (Pb/Sr) and Se atoms in p-type SnSe-9%Pb-1.2%Sr crystals with increasing temperature from 300 K to 698 K.